# Hest

0th

Percentile

##### Spherical Contact Distribution Function

Estimates the spherical contact distribution function of a random set.

Keywords
spatial, nonparametric
##### Usage
Hest(X, ...)
##### Arguments
X
The observed random set. An object of class "ppp", "psp" or "owin".
...
Arguments passed to as.mask to control the discretisation.
##### Details

The spherical contact distribution function of a stationary random set $X$ is the cumulative distribution function $H$ of the distance from a fixed point in space to the nearest point of $X$, given that the point lies outside $X$. That is, $H(r)$ equals the probability that X lies closer than $r$ units away from the fixed point $x$, given that X does not cover $x$.

For a point process, the spherical contact distribution function is the same as the empty space function $F$ discussed in Fest.

For Hest, the argument X may be a point pattern (object of class "ppp"), a line segment pattern (object of class "psp") or a window (object of class "owin"). It is assumed to be a realisation of a stationary random set.

The algorithm first calls distmap to compute the distance transform of X, then computes the Kaplan-Meier and reduced-sample estimates of the cumulative distribution following Hansen et al (1999).

##### Value

• An object of class "fv", see fv.object, which can be plotted directly using plot.fv.

Essentially a data frame containing five columns:

• rthe values of the argument $r$ at which the function $H(r)$ has been estimated
• rsthe reduced sample'' or border correction'' estimator of $H(r)$
• kmthe spatial Kaplan-Meier estimator of $H(r)$
• hazardthe hazard rate $\lambda(r)$ of $H(r)$ by the spatial Kaplan-Meier method
• rawthe uncorrected estimate of $H(r)$, i.e. the empirical distribution of the distance from a fixed point in the window to the nearest point of X

##### References

Baddeley, A.J. Spatial sampling and censoring. In O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. van Lieshout (eds) Stochastic Geometry: Likelihood and Computation. Chapman and Hall, 1998. Chapter 2, pages 37-78. Baddeley, A.J. and Gill, R.D. The empty space hazard of a spatial pattern. Research Report 1994/3, Department of Mathematics, University of Western Australia, May 1994.

Hansen, M.B., Baddeley, A.J. and Gill, R.D. First contact distributions for spatial patterns: regularity and estimation. Advances in Applied Probability 31 (1999) 15-33.

Ripley, B.D. Statistical inference for spatial processes. Cambridge University Press, 1988.

Stoyan, D, Kendall, W.S. and Mecke, J. Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.

##### See Also

Fest

• Hest
##### Examples
X <- runifpoint(42)
H <- Hest(X)
Y <- rpoisline(10)
H <- Hest(Y)
data(heather)
H <- Hest(heather\$coarse)
Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)

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